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Poincaré’s philosophy of geometry and its reception in the twentieth-century philosophy of science

University of British Columbia

Most twentieth-century philosophers of science, whose works are surveyed in this work, argue that Poincaré’s most consequential contribution to the philosophy of geometry is his discovery that one can choose one’s favourite geometric language/framework in order to formulate physical theories not based on epistemological considerations (truth) but practical ones (convenience). According to these philosophers, Poincaré uses such freedom in choosing the geometric framework to argue that axioms of (physical) geometry – which (allegedly) describes the (spatial) structure of the scene in which the drama of physics unfolds (physical space) – are a matter of convention. The main goal of this work is, however, to establish that, properly understood in its intellectual and historical context, Poincaré’s contribution to the philosophy of geometry is not limited to offering a novel epistemological category – that is, conventional truths. Instead, I argue that Poincaré offers a comprehensive philosophical account of geometry dealing with all major philosophical questions about or raised by geometry: (1) What kind of objects are geometric objects? (2) What can be known about geometric objects? How is this kind of knowledge possible? What is the epistemic status of this kind of knowledge? (3) How are the geometric concepts acquired? (4) How can one explain the applicability of geometry? How is it possible to use geometry to describe/explain the natural world? What is the nature of the relation between physics and geometry? We will see how Poincaré uses four elements of his account of geometry – that is, (i) his theory of the nature of geometry and geometric objects where the notion of ‘free mobility’ plays an essential role; (ii) his epistemic stance according to which the axioms of geometry are conventions; (iii) his theory of the origin of spatial intuitions and geometric concepts in which the notion of group plays a constituting role; and (iv) his stance regarding the relation between geometry and physics, that is the freedom in choosing the geometric language/framework for describing the spatial relations in theories of physics – to answer these questions.

Text

2020-05-04

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/74275

Philosophy

University of British Columbia

UBCV

http://creativecommons.org/licenses/by-nc-nd/4.0/